## Posts tagged ‘GPS’

### Never Ask a Mathematician for Directions

I spent my formative years in a very rural county. Roads didn’t have names, or at least they didn’t have road name signs.

In college, my urban friends used to claim that if you asked someone in my hometown for directions, they’d say:

Go about a half mile, and turn left at Old Man Johnson’s farm. Then take a right at the huckleberry tree.

That very well may be true, but it’s no worse than the directions you might be given by a mathematician:

Well, you’re facing the wrong way, so do a reflection about this cross street. Go about 0.628397154 miles, then rotate π/2 radians and travel orthogonally to your previous vector for 600 light-nanoseconds. But they’ve got radar on that road, so keep your speed between 7

^{2}and 4^{3}miles per hour. Turn left, and you should reach your destination in 2.4 minutes ± 0.3%, if you maintain an average speed of 46.8 mph.

Now, that’s bad. But at least I could understand all of it. Which is more than I can say for the directions that Google Maps provided yesterday. Traveling through the suburbs near Washington, DC, I had just crossed MacArthur Boulevard, and I was heading southwest on Arizona Avenue. As you can see from the screenshot below, Google Maps was suggesting that I turn right on Carolina Place, right on Galena Place, right on Dorsett Place, and then left on Arizona. In essence, it suggested that I reverse direction to take a 10-mile, 45-minute route.

I ignored that suggestion. Instead, I stayed on Arizona Avenue with the intention of turning right onto Canal Road in a quarter-mile. Just as I passed Carolina Place, Google Maps said that it was “Rerouting…,” and within 15 seconds, it confirmed that I had made the correct choice:

By ignoring Google Maps, I shaved 3.8 miles and 23 minutes from my commute.

WTF?

My speculation is that Google Maps attempts to avoid my chosen route because it follows Canal Road, which parallels the C&O Canal National Historic Park; it requires me to cross Chain Bridge, which offers a beautiful view of the Potomac River; and it then winds through an affluent neighborhood, where I can feel safe on tree-lined streets with elegant homes. Honestly, who would choose that when Google Maps is offering double the travel time and an opportunity to drive on the beltway?

I once asked Google Maps which highway I should take to California. It replied…

Oh, yeah. Root 66.

The logic employed by Google Maps reminds me of a college friend…

He would always accelerate when coming to an intersection, race through it, and then brake on the other side. I asked him why he went so fast through intersections. He replied, “Well, statistics show that more accidents happen at intersections, so I try to spend less time there.”

### Math in France

Driving through the French countryside using smartphone GPS for navigation is a lot like driving through rural Pennsylvania with my redneck cousin riding shotgun — there is a significant lack of sophistication, an ample amount of mispronunciation, and myriad grammatical errors.

In Pennsylvania:

Take that there right onto See-Quo-Eye-Ay (Sequoia) Drive.

In France:

At the roundabout, take the second right toward Ow-Bag-Nee (Aubagne).

Take D51 to Mar-Sigh-Less (Marseilles).

And of course, the GPS pronounced the coastal town of Nice like the adjective you’d use to describe your grandmother’s sweater, though it should sound more like the term you’d use to describe your brother’s daughter.

I was half expecting the computer voice to exclaim,

Hey, cuz, watch this!

Otherwise, the rest of my recent week-long trip to the south of France was intellectually and often mathematically stimulating. The image below shows a -1 used to describe an underground floor (parking) in a hotel:

And though I didn’t get a picture, the retail floor of the parking garage at the Palais de Papes in Avignon was labeled 0, with the three floors below for parking labeled -1, -2, and -3.

This is a country that does **not** fear negative integers.

I also noticed that the nuts on fire hydrants in Aix-en-Provence were squares.

The nuts on American hydrants used to be squares, until hoodlums realized that two pieces of strong wood could be used to remove them, release water into the streets, and create an impromptu pool party for the neighborhood. As a result, pentagonal nuts are now used on most hydrants.

Alas, an adept hoodlum can even remove pentagonal nuts, so some localities have replaced them with Reuleaux triangle nuts, like the ones on hydrants outside the Philadelphia convention center, which can only be removed with a specially forged wrench.

But perhaps the most mathematical fun that France has to offer is the Celsius scale. While there, our cousins taught my sons a poem for intuitively understanding the Celsius scale:

30 is hot,

20 is nice,

10 is cold,

and 0 is ice.

And I was able to teach them a formula for estimating Fahrenheit temperatures, which is easy to calculate and provides a reasonable approximation:

Double the (Celsius) temperature, then add 30.

Or algebraically,

F= 2C+ 30

The actual rule for converting from Fahrenheit to Celsius is more familiar to most students:

F= 1.8C+ 32

This rule, however, sucks. It’s not easy to mentally multiply by 1.8.

My sons were not convinced that the rule for estimating would give a close enough approximation. I showed them a table of values from Excel:

I also showed them a graph with the lines *y* = 1.8*x* + 32 and *y* = 2*x* + 30:

With both representations, it’s fairly clear that the estimate is reasonably close to the actual. For the normal range of values that humans experience, the estimate is typically within 5°. Even for the most extreme conditions — the coldest recorded temperature on Earth was -89°C in Antartica, and the hottest recorded temperature was 54°C in Death Valley, CA — the Fahrenheit estimates are only off by 9° and 20°, respectively. That’s good enough for government work.

And here’s a puzzle problem for an Algebra classroom, using this information.

The Fahrenheit and Celsius scales are related by the formula

F= 1.8C+ 32. But a reasonable estimate of the Fahrenheit temperature can be found by doubling the Celsius temperature and adding 30. For what Celsius temperature in degrees will the actual Fahrenheit temperature equal the estimated Fahrenheit temperature?

It’s not a terribly hard problem… especially if you look at the table of values above.